Skeletal shape representations, in spite of their structural instabilities, have proven themselves as effective representation schemes for recognition and classification of visual shapes. They capture part structure in a compact and natural way and provide insensitivity to visual transformations such as occlusion and articulation of parts. In this thesis, we explore the potential use of disconnected skeleton representation for shape recognition and shape classification. Specifically, we first investigate the importance of contextual information in recognition where we extend the previously proposed disconnected skeleton based shape matching methods in different ways by incorporating category knowledge into matching process. Unlike the view in syntactic matching of shapes, our interpretation differentiates the semantic roles of the shapes in comparison in a way that a query shape is being matched with a database shape whose category is known a priori. The presence of context, i.e. the knowledge about the category of the database shape, influences the similarity computations, and helps us to obtain better matching performance. Next, we build upon our category-influenced matching framework in which both shapes and shape categories are represented with depth-1 skeletal trees, and develop a similarity-based shape classification method where the category trees formed for each shape category provide a reference set for learning the relationships between categories. As our classification method takes into account both within-category and between-category information, we attain high classification performance. Moreover, using the suggested classification scheme in a retrieval task improves both the efficiency and accuracy of matching by eliminating unrelated comparisons.

In this paper we introduce two classes of functions called weakly δ -open and weakly δ -closed functions. We obtain their characterizations, their basic properties and their relationships with other types of functions between topological spaces.

Indiana University-Purdue University Indianapolis (IUPUI) / The power transmission network is stretched thin in Western North America. When generators or substations fault, the resultant cascading failures can diminish transmission capabilities across wide regions of the continent. This thesis examined several methods of determining one-shot controls based on frequency decline in electrical generators to reduce the effect of one or more phase faults and tripped generators. These methods included criteria based on indices calculated from frequency measured at the controller location. These indices included criteria based on local modes and the rate of change of frequency. This thesis primarily used particle swarm optimization (PSO) with inertia to determine a well-adapted set of parameters. The parameters included up to three thresholds for indices calculated from frequency. The researchers found that the best method for distinguishing between one or more phase faults used thresholds on two Fourier indices. Future lines of research regarding one-shot controls were considered. A method that distinguished nearby tripped generators from one or more phase faults and load change events was proposed. This method used a moving average, a negative threshold for control, and a positive threshold to reject control. The negative threshold for the moving average is met frequently during any large transient event. An additional index must be used to distinguish loss of generation events. This index is the maximum value of the moving average up to the present time and it is good for distinguishing loss of generation events from transient swings caused by other events. This thesis further demonstrated how well a combination of controls based on both rate of change of frequency and local modes reduces instability of the network as determined by both a reduction in RMSGA and control efficiency at any time after the events. This thesis found that using local modes is generally useful to diagnose and apply one-shot controls when instability is caused by one or more phase faults, while when disconnected generators or reduced loads cause instability in the system, the local modes did not distinguish between loss of generation capacity events and reduced load events. Instead, differentiating based on the rate of change of frequency and an initial upward deflection of frequency or an initial downward deflection of frequency did distinguish between these types of events.

Security is essential to communication between entities in the internet. Delay tolerant and disconnected Mobile Ad Hoc Networks (MANET) are a class of networks characterized by high end-to-end path latency and frequent end-to-end disconnections and are often termed as challenged networks. In these networks nodes are sparsely populated and without the existence of a central server, acquiring global information is difficult and impractical if not impossible and therefore traditional security schemes proposed for MANETs cannot be applied. This thesis reports trust management schemes for peer to peer (P2P) application in delay tolerant disconnected MANETs. Properties of a profile based file sharing application are analyzed and a framework for structured P2P overlay over delay tolerant disconnected MANETs is proposed. The framework is implemented and tested on J2ME based smart phones using Bluetooth communication protocol. A light weight Content Driven Data Propagation Protocol (CDDPP) for content based data delivery in MANETs is presented. The CDDPP implements a user profile based content driven P2P file sharing application in disconnected MANETs. The CDDPP protocol is further enhanced by proposing an adaptive opportunistic multihop content based routing protocol (ORP). ORP protocol considers the store-carry-forward paradigm for multi-hop packet delivery in delay tolerant MANETs and allows multi-casting to selected number of nodes. Performance of ORP is compared with a similar autonomous gossiping (A/G) protocol using simulations. This work also presents a framework for trust management based on dynamicity aware graph re-labelling system (DA-GRS) for trust management in mobile P2P applications. The DA-GRS uses a distributed algorithm to identify trustworthy nodes and generate trustable groups while isolating misleading or untrustworthy nodes. Several simulations in various environment settings show the effectiveness of the proposed framework in creating trust based communities. This work also extends the FIRE distributed trust model for MANET applications by incorporating witness based interactions for acquiring trust ratings. A witness graph building mechanism in FIRE+ is provided with several trust building policies to identify malicious nodes and detect collusive behaviour in nodes. This technique not only allows trust computation based on witness trust ratings but also provides protection against a collusion attack. Finally, M-trust, a light weight trust management scheme based on FIRE+ trust model is presented.

The power transmission network is stretched thin in Western North America. When generators or substations fault, the resultant cascading failures can diminish transmission capabilities across wide regions of the continent. This thesis examined several methods of<br><div>determining one-shot controls based on frequency decline in electrical generators to reduce the effect of one or more phase faults and tripped generators. These methods included criteria based on indices calculated from frequency measured at the controller location. These indices included criteria based on local modes and the rate of change of frequency.</div><br>This thesis primarily used particle swarm optimization (PSO) with inertia to determine a well-adapted set of parameters. The parameters included up to three thresholds for indices calculated from frequency. The researchers found that the best method for distinguishing between one or more phase faults used thresholds on two Fourier indices. Future lines of research regarding one-shot controls were considered.<br><div><br></div><div>A method that distinguished nearby tripped generators from one or more phase faults and load change events was proposed. This method used a moving average, a negative<br></div>threshold for control, and a positive threshold to reject control. The negative threshold for the moving average is met frequently during any large transient event. An additional index must be used to distinguish loss of generation events. This index is the maximum value of the moving average up to the present time and it is good for distinguishing loss of<br>generation events from transient swings caused by other events.<br><br><div>This thesis further demonstrated how well a combination of controls based on both rate of change of frequency and local modes reduces instability of the network as determined by both a reduction in RMSGA and control efficiency at any time after the events.</div><br>This thesis found that using local modes is generally useful to diagnose and apply one-shot controls when instability is caused by one or more phase faults, while when disconnected generators or reduced loads cause instability in the system, the local modes did not distinguish between loss of generation capacity events and reduced load events. Instead, differentiating based on the rate of change of frequency and an initial upward deflection of frequency or an initial downward deflection of frequency did distinguish between these types of events.

La segmentation d'image constitue une étape importante dans le traitement d'image et de nombreuses questions restent ouvertes. Il a été montré récemment, dans le cas d'une segmentation à deux régions homogènes, que l'utilisation de contours actifs polygonaux fondés sur la minimisation d'un critère issu de la théorie de l'information permet d'aboutir à un algorithme ultra-rapide qui ne nécessite ni paramètre à régler dans le critère d'optimisation, ni connaissance a priori sur les fluctuations des niveaux de gris. Cette technique de segmentation rapide et non supervisée devient alors un outil élémentaire de traitement.L'objectif de cette thèse est de montrer les apports de cette brique élémentaire pour la conception de nouvelles techniques de segmentation plus complexes, permettant de dépasser un certain nombre de limites et en particulier :- d'être robuste à la présence dans les images de fortes inhomogénéités ;- de segmenter des objets non connexes par contour actif polygonal sans complexifier les stratégies d'optimisation ;- de segmenter des images multi-régions tout en estimant de façon non supervisée le nombre de régions homogènes présentes dans l'image.Nous avons pu aboutir à des techniques de segmentation non supervisées fondées sur l'optimisation de critères sans paramètre à régler et ne nécessitant aucune information sur le type de bruit présent dans l'image. De plus, nous avons montré qu'il était possible de concevoir des algorithmes basés sur l'utilisation de cette brique élémentaire, permettant d'aboutir à des techniques de segmentation rapides et dont la complexité de réalisation est faible dès lors que l'on possède une telle brique élémentaire. / Image segmentation is an important step in many image processing systems and many problems remain unsolved. It has recently been shown that when the image is composed of two homogeneous regions, polygonal active contour techniques based on the minimization of a criterion derived from information theory allow achieving an ultra-fast algorithm which requires neither parameter to tune in the optimized criterion, nor a priori knowledge on the gray level fluctuations. This algorithm can then be used as a fast and unsupervised processing module. The objective of this thesis is therefore to show how this ultra-fast and unsupervised algorithm can be used as a module in the conception of more complex segmentation techniques, allowing to overcome several limits and particularly:- to be robust to the presence of strong inhomogeneity in the image which is often inherent in the acquisition process, such as non-uniform illumination, attenuation, etc.;- to be able to segment disconnected objects by polygonal active contour without complicating the optimization strategy;- to segment multi-region images while estimating in an unsupervised way the number of homogeneous regions in the image.For each of these three problems, unsupervised segmentation techniques based on the optimization of Minimum Description Length criteria have been obtained, which do not require the tuning of parameter by user or a priori information on the kind of noise in the image. Moreover, it has been shown that fast segmentation techniques can be achieved using this segmentation module, while keeping reduced implementation complexity.

Gitter QCD ist ein erfolgreiches Instrument zur nicht-perturbativen Berechnung von QCD Observablen. Die hierfür notwendige Auswertung des QCD Pfadintegrals besteht aus zwei Teilen: Zuerst werden Stützstellen generiert, an denen danach das Pfadintegral ausgewertet wird. In der Regel werden für den ersten Teil Markov-chain Monte Carlo (MCMC) Methoden verwendet, die für die meisten Anwendungen sehr gute Ergebnisse liefern, aber auch Probleme wie eine langsame Fehlerskalierung und das numerische Vorzeichenproblem bergen. Der zweite Teil beinhaltet die Berechnung von Quark zusammenhängenden und unzusammenhängenden Diagrammen. Letztere tragen maßgeblich zu physikalischen Observablen bei, jedoch leidet deren Berechnung an großen Fehlerabschätzungen. In dieser Arbeit werden Methoden präsentiert, um die beschriebenen Schwierigkeiten in beiden Auswertungsteilen des QCD Pfadintegrals anzugehen und somit Observablen effizienter beziehungsweise genauer abschätzen zu können. Für die Berechnung der unzusammenhängenden Diagramme haben wir die Methode der exakten Eigenmodenrekonstruktion mit Deflation getestet und konnten eine 5.5 fache Verbesserung der Laufzeit erreichen. Um die Probleme von MCMC Methoden zu adressieren haben wir die rekursive numerische Integration zur Vereinfachung von Integralauswertungen getestet. Wir haben diese Methode, kominiert mit einer Gauß-Quadraturregel, auf den eindimensionalen quantenmechanischen Rotor angewandt und konnten exponentiell skalierende Fehlerabschätzungen erreichen. Der nächste Schritt ist eine Verallgemeinerung zu höheren Raumzeit Dimensionen. Außerdem haben wir symmetrisierte Quadraturregeln entwickelt, um das Vorzeichenproblem zu umgehen. Wir haben diese Regeln auf die eindimensionale QCD mit chemischem Potential angewandt und konnten zeigen, dass sie das Vorzeichenproblem beseitigen und sehr effizient auf Modelle mit einer Variablen angewendet werden können. Zukünftig kann die Effizienz für mehr Variablen verbessert werden. / Lattice QCD is a very successful tool to compute QCD observables non-perturbatively from first principles. The therefore needed evaluation of the QCD path integral consists of two parts: first, sampling points are generated at which second, the path integral is evaluated. The first part is typically achieved by Markov-chain Monte Carlo (MCMC) methods which work very well for most applications but also have some issues as their slow error scaling and the numerical sign-problem. The second part includes the computation of quark connected and disconnected diagrams. Improvements of the signal-to-noise ratio have to be found since the disconnected diagrams, though their estimation being very noisy, contribute significantly to physical observables. Methods are proposed to overcome the aforementioned difficulties in both parts of the evaluation of the lattice QCD path integral and therefore to estimate observables more efficiently and more accurately. For the computation of quark disconnected diagrams we tested the exact eigenmode reconstruction with deflation method and found that this method resulted in a 5.5-fold reduction of runtime. To address the difficulties of MCMC methods, we tested the recursive numerical integration method, which simplifies the evaluation of the integral. We applied the method in combination with a Gauss quadrature rule to the one-dimensional quantum-mechanical rotor and found that we can compute error estimates that scale exponentially to the correct result. A generalization to higher space-time dimensions can be done in the future. Additionally, we developed the symmetrized quadrature rules to address the sign-problem. We applied them to the one-dimensional QCD with a chemical potential and found that this method is capable of overcoming the sign-problem completely and is very efficient for models with one variable. Improvements of the efficiency for multi-variable scenarios can be made in the future.

<p>Ako je<em> L </em>relacijski jezik, kondenzacioni pretporedak na skupu<em> Int</em>_L <em>(X)</em> svih <em>L-</em>interpretacija nad domenom <em>X,</em> dat je sa: &rho;≼_c <em>&sigma;</em> ako postoji bijektivni homomorfizam (kondenzacija)<em> f:〈X,&rho;</em>〉&rarr;<em>〈X,&sigma;〉.</em> Odgovarajući antisimetrični količnik <em>〈Int_L</em> (X)/~_c,&le;_c〉 ~naziva se kondenzacioni poredak. Za proizvoljnu<em> L-</em>interpretaciju &rho;, klasa [&rho;]~_c&nbsp; je konveksno zatvorenje klase [&rho;]_&cong; u Booleovoj mreži 〈<em>IntL (X</em>),&sube;〉. Za <em>L</em>-interpretaciju &rho; reći ćemo da je jako reverzibilna (redom, reverzibilna, slabo reverzibilna) akko je klasa [&rho;]_&cong;&nbsp; (ili, ekvivalentno, klasa [&rho;]~_c)) singlton (redom, antilanac, konveksan skup) u Booleovoj mreži 〈<em>IntL (X)</em>,&sube;〉. U cilju ispitivanja poseta 〈<em>Int(_Lb</em>) (X)/~c,&le;c〉, za &rho;&isin;<em>Irrefl_X</em> uveden je skup D_&rho;:={[&rho;&cup;&Delta;_A ](~_c ):<em>A&sube;X</em>} i pokazano je kako je poduređenje 〈D_&rho;,&le;_c 〉 izomorfno određenom količniku partitivnog skupa<em> P(X)</em>. Fenomen reverzibilnosti relacijskih struktura igra istaknutu ulogu u istraživanju tog poduređenja.</p><p>U slučaju prebrojivog jezika <span id="cke_bm_1038S" style="display: none;">&nbsp;</span><em>L</em><span id="cke_bm_1038E" style="display: none;">&nbsp;</span> i prebrojivog domena <em>X</em>, pokazano je da su ~_c i [&rho;]~_canalitički skupovi u poljskim prostorima, redom, <em>Int_L(&omega;)&times;Int_L(&omega;) i Int_L (&omega;)</em>, i pomoću toga, pokazano ja da su, u slučaju prebrojivog jezika i domena, klase [&rho;]&cong;&nbsp; i [&rho;]~_c iste veličine, i da je to neki kardinal iz {1,&omega;,c}. Dalje je istražena hijerarhija između kondenzacione ekvivalencije, elementarne ekvivalencije, ekvimorfizma (bi-utopivosti) i drugih sličnosti <em>L-</em>struktura određenih nekim sličnostima njihovih monoida samoutapanja.</p><p>Naposletku, temeljno je istražen fenomen reverzibilnosti <em>L</em>-struktura. Data je karakterizacija jako reverzibilnih<em> L</em>-intepretacija kao onih čije su komponentne relacije definabilne formulama praznog jezika<em> L</em>_&empty;, bez kvantifikatora i parametara. Pokazano je kako su slabo reverzibilne interpretacije upravo one koje imaju svojstvo Cantor-Schrӧder-Bernstein (kraće, svojstvo CSB) za kondenzacije.</p><p>Poseban naglasak stavljen je na detektovanje relevantnih klasa reverzibilnih struktura. Pri tome, prvo su proučene strukture koje su ekstremni elementi L_{&infin;&omega;}-definabilnih klasa interpretacija, pri određenim sintaktičkim ograničenjima, a zatim su istražene nepovezane<em> L</em>_b-strukture, gde je dato nekoliko karakterizacija njihove reverzibilnosti.</p> / <p>If <em>L</em> is a relational language, the condensational preorder on the set <em>Int_L (X)</em> of all <em>L-</em>interpretations over the domain<em> X</em>, is given with: &rho;≼_c &sigma; iff there exists a bijective homomorphism (condensation) <em>f:〈X,&rho;〉&rarr;〈X,&sigma;〉. </em>The corresponding antisymmetric quotient 〈<em>Int_L (X)/</em>~_<em>c</em>,&le;__c〉 will be called the condensational order. For any <em>L</em>-interpretation &rho;, the class<em> [&rho;]~_c )</em> is the convex closure of the class [<em>&rho;</em>]&cong; in the Boolean lattice 〈<em>IntL (X</em>),&sube;〉. An <em>L</em>-interpretation &rho; is said to be strongly reversible&nbsp; (respectively, reversible, weakly reversible) iff the class <em>[&rho;]</em>&cong;&nbsp; (or, equivalently, the class<em> [&rho;]~c )</em>) is a singleton (respectively, an antichain, a convex set) in the poset 〈 <em>IntL</em> <em>(X)</em>,&sube;〉. In order to investigate the poset 〈<em>Int_(Lb ) (X)/~c,&le;_c</em>〉, for &rho;&isin;<em> IrreflX</em> the following set is defined <em>D_&rho;</em>:={[&rho;&cup;&Delta;_A ]_~c :A&sube;X}. It is shown that the suborder 〈<em>D_&rho;,</em>&le;_c 〉 is isomorphic to a certain quotient of the power set <em>P(X)</em>. The phenomenon of reversibility plays prominent role in the investigation of that suborder.<br />In the case of a countable language<em> L</em> and a countable domain&nbsp; <em>X</em>, it is shown that ~c&nbsp; and [<em>&rho;]__~c&nbsp;</em>are analytic sets in the Polish spaces, respectively,<em> IntL (&omega;)&times; IntL (&omega;)</em> and <em>Int_L (&omega;)</em>, and, using those results, in the case of a countable language and domain it is shown that the classes <em>[&rho;]_</em>&cong;&nbsp; and <em>[&rho;]~_c&nbsp;</em>are of the same size, and that it is a cardinals from _{{1,&omega;,c}. N}ext, the hierarchy between condensational equivalence, elementary equivalence, equimorphism (bi- embedability) and other similarities of <em>L</em>-structures, determined by some similarities of their self-embedding monoids, is investigated.<br />In the last part, the phenomenon of reversibility of<em> L</em>-structures is investigated. Strongly reversible <em>L</em>-intepretations are characterized as those whose component relations are definable by the formulae of the empty language<em> L_&empty;, </em>without quantifiers and parameters. It is shown that weakly reversible interpretations are exactly those having the property Cantor-Schrӧder-Bernstein (shorter, the property CSB) for condensations.<br />Particular emphasis is put on detecting relevant classes of reversible structures. First, the structures that are extreme elements of<em> L</em>_{&infin;&omega;}-definable classes of interpretations, under certain syntactical restrictions, are investigated. Following that, disconnected Lb-structures are investigated, where several equivalents of their reversibility are proven.</p>